We've some rather simply tests for each of the distinct types of symmetry.

1. A graph will have symmetry around the x-axis if we get an equal equation while all the y's are replaced with -y.

2. A graph will have symmetry around the y-axis if we obtain an corresponding equation while all the x's are replaced along with -x.

3. A graph will have symmetry around the origin if we obtain an equivalent equation while all the y's are replaced through -y and all the x's are replaced through -x.

We will describe just what we mean through an "equivalent equation" while we reach an example of that. For the majority of the instance which we're liable to run across it will mean that it is precisely the similar equation.

Let's test a few equations for symmetry.  Note that we aren't going to graph these as most of them would actually be rather difficult to graph. The point of this instance is only to use the tests to find out the symmetry of each equation.